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**ANDS!** Oh dear. Well, at least you recognize this as a linear first order differential. It is the confusion on what your integrating factor is that is the problem. Remember, a differential is in linear form when it is written as:

$\displaystyle y'+P(x)+Q(x)=0$, with an integrating factor equal to $\displaystyle \mu = e^{\int P(x) dx}$.

Rewriting the equation so that it is in linear form we get:

$\displaystyle y'+\frac{3y}{x}=\frac{1}{x^{3}(x+2)}$

Thus, our integrating factor is $\displaystyle \mu = e^{\int \frac{3}(x) dx}$. From here you should see how things start to cancel out. If you need more help, post here.